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Entropic gravity

Entropic gravity is a theoretical framework proposing that gravity emerges not as a fundamental force but as an entropic phenomenon driven by the universe's tendency to maximize , rooted in holographic principles and theory. First articulated by Erik Verlinde in 2010, the theory posits that the positions of material bodies in space alter the distribution of microscopic information on a holographic screen, generating an analogous to thermodynamic forces like . This approach derives and the law of from first principles, suggesting that both and arise from entropy gradients rather than intrinsic properties of . At its core, entropic gravity relies on the holographic principle, which asserts that the information content of a volume of space can be encoded on its boundary surface, much like a hologram. Verlinde's model treats spacetime as emergent from underlying quantum degrees of freedom, where the entropy associated with these degrees changes as objects move, leading to a force proportional to the mass and inversely to the square of the distance between bodies. A key assumption is the Unruh temperature, linking acceleration to a thermal bath for an observer, which ties inertial motion to entropic considerations via the equivalence principle. Relativistically generalizing these ideas yields the Einstein field equations of general relativity, implying that entropic gravity could unify classical gravity with quantum mechanics at a deeper level. Since its inception, entropic gravity has inspired extensions addressing cosmic phenomena, such as and , by interpreting them as manifestations of entropic effects rather than exotic particles. For instance, recent models suggest that modified entropic forces could explain accelerated cosmic expansion without invoking a . In 2025, a novel formulation known as "Gravity from Entropy" derives dynamics directly from an entropic action coupling matter fields to geometry via quantum relative entropy, offering a pathway to . Experimental proposals, including tests with quantum atom clouds to detect predicted gravitational fluctuations, are emerging to probe these ideas, though the theory remains speculative and faces challenges in fully reproducing general relativity's predictions.

Overview and Significance

Definition and Core Concept

Entropic gravity proposes that is not a fundamental force but an emergent arising from the tendency of microscopic quantum states to maximize , akin to thermodynamic processes where order gives way to disorder. In this framework, introduced by physicist Erik Verlinde in 2010, gravitational attraction emerges as a consequence of changes in the associated with the positions and configurations of material bodies in . This view positions entropic gravity as a potential bridge between and , suggesting that the familiar pull of reflects underlying statistical behaviors rather than a primitive interaction. At its core, the mechanism of entropic gravity relies on emerging as a structure from , with information about the universe encoded on holographic screens—hypothetical surfaces that store proportional to their area. When masses approach each other, they displace these screens, leading to an increase in as the system seeks to maximize the number of accessible quantum microstates; this gradient then manifests as the observed gravitational force pulling the masses together. , which posits that the of a volume of space can be described by a theory on its boundary, underpins this emergent picture of . A key for entropic gravity draws from thermodynamic phenomena, such as across a semi-permeable or the elasticity of a polymer chain, where forces arise purely from configurational changes without requiring fundamental attractive interactions. In , for instance, particles diffuse to equalize concentrations and maximize , producing a pressure that mimics attraction; similarly, in entropic gravity, the drive toward higher configurations yields the of Newtonian gravity as an effective description. This entropic origin underscores gravity's role as a statistical outcome of dynamics, offering a unified perspective on forces in nature.

Motivations in Fundamental Physics

Entropic gravity emerges as a promising framework for unifying and by positing gravity as an information-theoretic effect rather than a fundamental of . This approach draws on , suggesting that the in a volume of space are encoded on its boundary, thereby treating gravitational phenomena as emergent from and entropy gradients. In this view, itself arises from underlying structures, potentially resolving the longstanding incompatibilities between and Einstein's theory of , where the latter fails at Planck scales and in singular regimes. A key motivation stems from quantum gravity inconsistencies, particularly the black hole information paradox, which arises when predicts information preservation during black hole evaporation via , while implies irreversible loss. Entropic gravity draws on holographic principles that interpret gravitational effects near horizons in entropic terms, potentially allowing information preservation on holographic screens. Furthermore, it engages with the holographic bound in , where the of a region is limited by its boundary area, providing a natural cutoff that prevents divergences in quantum gravity calculations and supports emergence from more fundamental quantum bits. The theory also targets the need for alternatives to and , which dominate the but introduce unseen components without direct detection. By deriving an additional "dark force" from entropy displacement in de Sitter spacetime, entropic gravity explains galactic rotation curves and cluster dynamics without invoking particles, aligning with observations previously attributed to . Notably, it naturally reproduces the (MOND) regime at low accelerations below a_0 \approx 1.2 \times 10^{-10} m/s², where Newtonian predictions deviate, offering a scale tied to the Hubble constant rather than an parameter. In , entropic gravity provides a where emerges from thermal volume-law contributions to at the , driving accelerated expansion without fine-tuned constants. This reduces reliance on the Lambda-CDM model's empirical parameters, such as the , by rooting cosmic evolution in , potentially unifying small-scale quantum effects with large-scale . Recent advancements as of 2025, such as the "Gravity from Entropy" formulation, further motivate this approach by deriving gravitational dynamics from quantum relative , advancing pathways to .

Historical Development

Early Thermodynamic Analogies to Gravity

In the 1970s, proposed that s possess an proportional to the area of their event horizons, given by S = \frac{A}{4 \ell_p^2} in , where A is the horizon area and \ell_p is the Planck length. This formulation implied that enforces a on information storage, as the scales with area rather than volume, suggesting a deep connection between gravitational phenomena and . Bekenstein's insight arose from considerations of the generalized , which posits that the total , including contributions, cannot decrease, thereby linking irreversible processes in to . Stephen Hawking extended this framework in the mid-1970s by demonstrating that black holes emit thermal radiation, now known as Hawking radiation, with a temperature T = \frac{\hbar \kappa}{2\pi k_B}, where \kappa is the surface gravity and k_B is Boltzmann's constant. This discovery provided a dynamical mechanism for black hole evaporation and reinforced the thermodynamic analogy, portraying event horizons as reservoirs of entropy that interact with quantum fields in the surrounding spacetime. Hawking's work established the four laws of black hole mechanics as direct analogs to the laws of thermodynamics, with horizon area playing the role of entropy and surface gravity akin to temperature, thus framing gravity as emergent from underlying thermal properties. By the 1990s, these insights inspired broader analogies between and gravitational effects beyond isolated horizons. Proposals emerged viewing gravitational acceleration as akin to heat flow in , where the implies that inertial motion in curved geometry mimics gradients, potentially arising from entropic displacements of microscopic . For instance, the , linking uniform acceleration to a thermal bath, was reinterpreted in entropic terms to suggest that local gravitational fields enforce thermodynamic consistency across observers. These ideas culminated in Ted 1995 derivation of Einstein's field equations from thermodynamic principles applied to local Rindler horizons, assuming proportional to horizon area and \delta Q = T dS. approach treated as a where variations in across null hypersurfaces yield the full nonlinear Einstein equations, highlighting gravity's roots in balance without invoking .

Precursors in Holographic and Quantum Information Theories

The emerged in the 1990s as a profound insight into the nature of , proposing that the information describing a volume of is fully encoded on its lower-dimensional boundary, with the of the system scaling with the boundary area rather than the enclosed volume. This concept addressed puzzles in physics, where the Bekenstein-Hawking formula indicated that is proportional to the event horizon's surface area, suggesting a fundamental limit on information storage that challenges traditional volume-based notions. introduced the idea in 1993, arguing that at the Planck scale implies a dimensional reduction, where physical in higher dimensions are holographically projected from a lower-dimensional theory to resolve infinities and unitarity issues in coupled to gravity. Leonard Susskind expanded on 't Hooft's conjecture in 1995, formalizing as a general framework applicable beyond black holes, positing that our observed three-dimensional is an effective description arising from processed on a two-dimensional surface, much like a hologram reconstructs a 3D image from 2D interference patterns. This principle implied that the fundamental of the might reside in boundary quantum , with bulk emerging as a derived structure, thereby bridging and through information-theoretic constraints. Susskind's interpretation integrated elements, emphasizing how the principle resolves the apparent loss of in black hole evaporation by encoding all details on the horizon. A pivotal realization of the holographic principle arrived in 1997 with Juan Maldacena's proposal of the AdS/CFT correspondence, establishing a precise duality between a quantum gravity theory in (d+1)-dimensional anti-de Sitter (AdS) space and a conformal field theory (CFT) on its d-dimensional boundary. In this framework, gravitational dynamics in the bulk AdS spacetime, including phenomena like black hole formation, are exactly equivalent to quantum correlations and entanglement in the non-gravitational CFT, implying that gravity and curved spacetime emerge holographically from the quantum entanglement structure of boundary degrees of freedom. The correspondence, derived in the large-N limit of superconformal field theories, provided the first concrete evidence that spacetime geometry could be an emergent phenomenon rooted in quantum information, without invoking higher dimensions or new physics beyond known quantum field theories. During the 2000s, advances in quantum information theory deepened these connections, particularly through the study of entanglement entropy in quantum field theories dual to gravitational systems. A landmark contribution was the Ryu-Takayanagi formula in 2006, which quantifies the entanglement entropy of a spatial region in the boundary CFT as proportional to the area of the minimal surface in the bulk AdS geometry homologous to that region, offering a direct geometric prescription for computing quantum entanglement via spacetime structure. This formula not only validated the holographic encoding of quantum information but also highlighted how bulk geometry encodes the entanglement patterns of boundary qubits, suggesting that spatial distances and connectivity in spacetime reflect underlying quantum correlations. The work built on earlier calculations of entanglement in conformal field theories, demonstrating universality in how quantum entanglement gives rise to area-law scaling, akin to the holographic bound. These insights paved the way for conceptual shifts toward viewing as emergent from networks in the late 2000s. Researchers began modeling as an "entanglement ," where nodes represent qubits or quantum bits and edges denote entanglement links, with the 's determining effective geometric relations and distances in the emergent bulk. This perspective, inspired by representations of quantum states, portrayed higher-dimensional geometry as arising from the of entanglement in lower-dimensional , aligning with the /CFT to suggest that local gravitational interactions stem from nonlocal processing. Such ideas underscored a transition from as a duality to a broader emergent , where 's fabric is woven from the quantum glue of entanglement.

Erik Verlinde's Theory

Fundamental Principles

Entropic gravity, as proposed by Erik Verlinde, posits that gravitational attraction emerges as an arising from the fundamental tendency of thermodynamic systems to maximize , rather than from a mediated by particles like gravitons. In this framework, is not a fundamental entity but emerges from an underlying microscopic structure encoded on holographic screens, where information is stored in discrete bits proportional to the screen's area. The displacement of massive objects alters the distribution of this information, leading to an gradient that manifests as the observed gravitational force. A central is the , where the of a spatial region are represented on its boundary surface, with each bit of corresponding to an area of l_p^2, where l_p is the Planck length, drawing from . When a test mass is displaced radially across such a screen, the change in the screen's area modifies the total stored on it, creating an imbalance that the system seeks to resolve by adjusting the position of the mass to restore the maximum configuration. This principle treats gravity as an emergent phenomenon tied to changes, without invoking a primitive . Another key principle incorporates the , which associates an acceleration a experienced by an observer with a corresponding T = \frac{\hbar a}{2\pi k_B c}, where \hbar is the reduced Planck's constant, k_B is Boltzmann's constant, and c is the , thereby linking inertial motion to thermal properties in the Rindler relevant to accelerated frames. This arises for observers in uniformly accelerated motion, interpreting the vacuum fluctuations as a thermal bath, which in Verlinde's theory provides the microscopic basis for the entropic response to curvature induced by mass. The entropy displacement for a particle of m moved a \Delta x perpendicular to the holographic screen is quantified as \Delta S = \frac{2\pi k_B m c \Delta x}{\hbar}, reflecting the change in the number of bits on the screen due to the mass-energy E = m c^2. This entropy variation drives an that acts to minimize the displacement and maximize the overall , effectively reproducing behavior as a statistical outcome of information redistribution rather than a fundamental force. Verlinde's formulation in his seminal paper thus eliminates the need for gravitons, positioning within a thermodynamic and information-theoretic .

Connection to the Holographic Principle

In Erik Verlinde's formulation of , serves as a foundational framework for deriving gravitational attraction as an emergent . The principle posits that the of a volume of space can be encoded on its boundary surface, implying that gravity arises from the of this information distribution rather than fundamental . Central to this connection are holographic screens, which are spherical surfaces surrounding massive bodies where the total is stored proportionally to the screen's area. For a screen of area A = 4\pi r^2, the S follows the Bekenstein-Hawking formula S = \frac{c^3 A}{4 G \hbar}, equivalent to \frac{A}{4 G \hbar} k_B c^3 in full units, representing the maximum information capacity in natural units where this corresponds to \frac{S}{k_B \ln 2} bits. These screens act as loci for holographic encoding, with the change driving the entropic dynamics of gravity. When a test m approaches such a screen, it displaces on the surface, inducing a change in area \Delta A and a corresponding variation \Delta S. This displacement leads to an satisfying F \Delta x = T \Delta S, where T is the associated Unruh temperature for the local , linking the microscopic information shift to the macroscopic gravitational pull. Verlinde's approach builds directly on interpretations of , particularly the of s and . Holographic screens are analogous to configurations, where open strings terminate on the screen and closed strings propagate in the emergent space, treating ordinary matter-induced as a dilute gas limit of these fundamental interactions. Unlike , where is a geometric property of , entropic emerges statistically from holographic gradients, providing a pathway to resolve quantum inconsistencies at Planck scales by rendering itself as a derived, non-fundamental entity.

Mathematical Derivations

Entropic Force Formulation

In Erik Verlinde's formulation of entropic gravity, the entropic force arises as a consequence of entropy gradients associated with the displacement of holographic screens in emergent spacetime. The general law for the entropic force \mathbf{F} acting on a test particle is given by \mathbf{F} = T \nabla S, where T represents the effective temperature of the holographic screen, and \nabla S denotes the gradient of the entropy S due to an infinitesimal displacement of the screen. This expression draws an analogy to thermodynamic forces, such as those in polymer elasticity or osmotic pressure, where changes in entropy drive macroscopic behavior. The T is identified with the Unruh temperature corresponding to the local a experienced by the particle near the holographic screen. For a spherical screen of radius r surrounding a M, the acceleration is the Newtonian value a = \frac{GM}{r^2}, yielding T = \frac{\hbar a}{2\pi k_B c} = \frac{\hbar G M}{2\pi k_B c r^2}, with \hbar as the reduced Planck's constant, k_B as Boltzmann's constant, and c as the . This assignment links the entropic framework directly to in curved spacetime via the . The S on the holographic screen is proportional to the encoded on its surface area A, following . The number of bits N on the screen is N = \frac{A c^3}{G \hbar}, where c is the , reflecting the Bekenstein-Hawking entropy bound. For a small \Delta x of a test m perpendicular to the screen, the change in is \Delta S = \frac{2\pi k_B m c}{\hbar} \Delta x, arising from the shift in the position of the mass relative to the screen's . Thus, \nabla S = \frac{\partial S}{\partial x} = \frac{2\pi k_B m c}{\hbar}, providing the needed for the force law. This entropic force formulation primarily applies to non-relativistic scenarios, where holographic screens are static and the motion of particles is slow compared to c. Relativistic extensions incorporate induced gauge fields on the screens, which modify the entropy distribution and connect to the full Einstein equations of general relativity.

Derivation of Newton's Law

In Erik Verlinde's formulation of entropic gravity, the derivation of Newton's law begins with the displacement of a test mass m near a holographic screen, which leads to a change in the entropy associated with the screen's information content. The entropy displacement \Delta S for the test mass is given by \Delta S = \frac{2\pi k_B m c}{\hbar} \Delta x, where k_B is Boltzmann's constant, c is the speed of light, \hbar is the reduced Planck's constant, and \Delta x is the radial displacement of the mass. This expression arises from the holographic principle, where the entropy is proportional to the area A of the screen, related to the displacement via the area-radius correspondence \Delta A = 8\pi R \Delta x for a spherical screen of radius R, and incorporating the number of bits N = A c^3 / (G \hbar) on the screen. The entropic force emerges from the thermodynamic requirement that the total entropy remains constant (dS = 0) during the displacement in equilibrium, implying that the mechanical work done by the force balances the entropic change: F \Delta x = T \Delta S, or equivalently, F = T \frac{dS}{dx}. Here, T is the effective Unruh temperature associated with the acceleration at the screen. Substituting the entropy gradient dS/dx = 2\pi k_B m c / \hbar yields F = T (2\pi k_B m c / \hbar). To connect this to gravity, the temperature T is determined from the applied to the energy E = M c^2 (where M is the enclosed by the screen) distributed over the N bits on the screen: E = \frac{1}{2} N k_B T. With N = A c^3 / (G \hbar) and A = 4\pi R^2, this gives T = \frac{\hbar a}{2\pi k_B c}, where a is the . For a gravitational field, a = G M / R^2, so T = \frac{\hbar G M}{2\pi k_B c R^2}. Substituting this into the force expression results in F = \frac{G M m}{R^2}, which exactly reproduces Newton's law of universal gravitation in the low-acceleration, non-relativistic limit. This derivation holds under assumptions such as the validity of the holographic principle and equipartition of microscopic degrees of freedom on the screen.

Modern Extensions

Quantum Relative Entropy Approaches

In the years following Erik Verlinde's entropic gravity proposal, researchers have explored quantum relative entropy as a foundational tool to derive gravitational effects from quantum information principles. A seminal 2025 contribution is the paper "Gravity from Entropy" by Ginestra Bianconi, which posits that gravity emerges from the quantum relative entropy S_{\text{rel}} between the actual spacetime state and a reference flat spacetime state. This relative entropy, a measure of the distinguishability between two quantum states, quantifies deviations from flat geometry and serves as the basis for an entropic action principle. Bianconi's framework constructs the action as an integral over the relative density, given by S = \int S_{\text{rel}} \, dV, where the integration is over volume. Varying this with respect to the metric yields modified that incorporate quantum corrections, such as terms arising from entanglement gradients. These equations reduce to in the classical limit but introduce emergent curvature tied directly to disparities, offering a pathway to unify with . The framework introduces a "G-field" as multipliers, leading to a dressed Einstein-Hilbert with an emergent positive ; further research may clarify its potential role in . An October 2025 follow-up explores the thermodynamic foundations of this Gravity from (GfE) theory, interpreting as a phenomenon encoding information in metric . Complementing this, a 2025 study by Melvin M. Vopson in AIP Advances proposes that arises from optimization processes in a computational model. Here, is conceptualized as a where gravitational attraction enforces the minimization of information among matter distributions, akin to data compression in computational systems. This approach treats reduction as a universal optimization rule, with manifesting as the force that clusters information to lower overall computational complexity. Vopson's model has drawn criticism, including a commentary by physicist Sabine Hossenfelder, to which Vopson has responded. Unlike Verlinde's original , which relies on holographic screen and classical thermodynamic analogies, these quantum relative methods integrate full metrics, such as differences, enabling more robust resolutions to information paradoxes through state distinguishability.

Cosmological Applications and Explanations

In entropic gravity theories, modifications to the standard Friedmann equations arise from entropic corrections to the holographic entropy-area relation, leading to an effective cosmological model that incorporates an additional term mimicking dark energy without invoking a cosmological constant. Specifically, the modified Friedmann equation for a flat universe takes the form H^2 = \frac{8\pi G \rho}{3} + \Lambda_{\text{ent}}, where the entropic term \Lambda_{\text{ent}} \propto \frac{a_0^2}{a^2} emerges from the scale-dependent entropy, providing a natural explanation for the observed accelerated expansion. This approach, explored in modified entropic cosmology (MEC), allows the model to describe the universe's dynamics from early radiation-dominated epochs to late-time acceleration solely through entropic effects on spacetime geometry. A key application of entropic gravity lies in its potential to explain phenomena without non-baryonic particles, particularly at low accelerations where emergent forces dominate galactic dynamics. In this framework, the transitions to a regime where F \approx \frac{\sqrt{G M a_0}}{r} for accelerations below a critical a_0 \approx 1.2 \times 10^{-10} \, \text{m/s}^2, yielding flat curves that match observations of spiral galaxies and systems without additional mass components. For instance, analyses of low-surface-brightness galaxies demonstrate that this entropic correction reproduces the observed profiles, attributing the "missing mass" to an emergent gravitational effect tied to the displacement of information entropy in the holographic screen. The MEC model of 2025 has been tested against cosmological data, showing consistency with anisotropies from Planck 2018, , supernovae observations, and the SH0ES measurement of the Hubble constant, outperforming the ΛCDM model and alleviating the Hubble tension through adjusted entropic scaling in the early universe.

Criticisms and Tests

Theoretical Objections

One prominent theoretical objection to entropic gravity arises from the unphysically large entropy changes required to account for ordinary gravitational interactions. In Erik Verlinde's formulation, the gravitational emerges from an entropy displacement on holographic screens, but such formulations face challenges in maintaining conservative forces for macroscopic systems without inconsistencies. Further thermodynamic inconsistencies undermine the framework's consistency with fundamental laws. The cited work demonstrates that assigning thermodynamic properties to surfaces away from event horizons—central to entropic gravity's holographic screens—leads to violations of of . Specifically, ordinary surfaces fail to satisfy the relation \delta M = \frac{1}{8\pi} \int \kappa \, \delta (dA), indicating they lack a valid variable like , except in fully spherically symmetric cases. This critique highlights a foundational flaw in extending entropic principles beyond horizons. Holographic aspects of entropic gravity also face significant conceptual challenges, particularly the lack of a clear of microscopic underlying the screens. While the theory posits that on these screens arises from encoded holographically, the precise mapping from nonlocal microstates to local particle positions remains undefined, leading to inconsistencies in how screen fragments describe emergent . Moreover, the approach fails to fully derive the equations of in arbitrary curved spacetimes, as it struggles to reconstruct motion for systems with charges, , or non-maximal screen , restricting its applicability to idealized spherical symmetries akin to black holes. Recent analyses continue to underscore difficulties in rigorously defining "cosmic entropy" for emergent gravitational forces. A 2025 review notes that while entropic gravity invokes holographic entanglement to explain large-scale , ambiguities persist in specifying the underlying microscopic and model, particularly for cosmic-scale applications where entanglement networks and two-dimensional screens lack precise formulation. These unresolved issues perpetuate about the theory's foundational validity.

Experimental and Observational Evidence

Entropic gravity, through its alignment with Modified Newtonian Dynamics (MOND)-like behaviors at low accelerations, has been tested against galaxy rotation curves, where it shows partial support. For instance, analysis of isolated dwarf galaxies indicates that emergent gravity predictions match observed maximum velocities reasonably well for systems around 100 km/s, though underpredicting for faster rotators and overpredicting for slower ones. However, these alignments face contradictions from solar system-scale observations, such as wide binary stars observed via Gaia data. Results from these studies are debated, with some analyses exhibiting orbital dynamics favoring Newtonian gravity over MOND predictions at low accelerations, while others support MOND-like behavior. Gravitational lensing in galaxy clusters provides mixed evidence for entropic gravity. In contrast, the collision, observed in 2006, demonstrates a clear separation between baryonic gas and gravitational mass peaks, strongly favoring particle interpretations over modified scenarios like entropic gravity, as the latter struggles to decouple lensing from visible matter. Recent theoretical extensions of entropic gravity link it to quantum coherence, predicting resolutions to decoherence puzzles in macroscopic superpositions. Entropic models propose that underlying qubit networks interact with massive objects in Schrödinger's cat-like states, inducing decoherence by aligning or redistributing to maximize , potentially testable in lab settings with superconducting s. In cosmological contexts, modified entropic gravity models from 2025 show promising fits to data from Planck 2018, outperforming the standard ΛCDM model in addressing the Hubble tension without , though implications for galaxy cluster dynamics remain under exploration and await verification from observations.

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